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Gear cutting machines with pitch error correction mechanisms

Milling man

Hot Rolled
Joined
Aug 6, 2021
Location
Moscow, Russia
Hello everyone, dear colleagues.
It is no secret that with the advent of CNC systems, entire classes of mechanisms disappeared into oblivion. And if the fundamental design of milling, turning, cylindrical or surface grinding machines has changed quite little, then machines for processing gears, grinding threads or grinding holes with precise coordinates have changed quite a lot.
Today I want to talk about the mechanisms for correcting angular pitch errors on machines for processing gears: gear hobbing machines or gear grinding machines with a grinding wheel in the form of a worm.
I came to metalworking at a time when all these amazing and complex miracles of mechanical engineering were almost no longer in existing industries. Therefore, I did not have the pleasure of working with such machines.
I hope that maybe one of the forum participants can tell me the models of gear-processing machines that had mechanical systems for correcting errors in the angular pitch of the teeth. I have so far found two suitable gear hobbing machines that were made in the USSR, but I cannot find documentation from these machines to study the device in detail, only a kinematic diagram and a brief description. In these machines, the workpiece is rotated by a worm gear (as in most mechanical gear hobbing machines), but between the block of replaceable gears and the worm there is an error correction mechanism for the worm gear. Two round cams - one for correcting errors of the worm wheel, makes one full revolution per revolution of the worm wheel. And the second cam, to correct worm errors, makes one full revolution per revolution of the worm.
About 2 years ago I saw some video on YouTube of a gear grinding machine with a grinding worm - and it was on that machine that I first saw such a mechanical angular pitch correction system. Unfortunately, I couldn't find that same video :(
In general, if someone remembers a similar machine or at least something about such equipment, it would be great. Well, if someone can share the documentation for such a machine, that would be just incredibly cool.
 
I have all the manuals for my 1980's 300mm Overton hobber. I don't recall it having a mechanism for correcting pitch errors, but it has dynamic hob shift, multi pass and a myriad of complicated electro-hydro-mechanical excitement. I'll skim the manual again for something like that, it may be in there somewhere and I missed it.
 
I am curious about what you mean by pitch errors. Do you mean cyclic variations in the angular movement of the worm wheel for EACH turn of the worm?

Or what?
 
I am curious about what you mean by pitch errors. Do you mean cyclic variations in the angular movement of the worm wheel for EACH turn of the worm? Or what?
All I can think is, he means tooth spacing errors. At least that's what it's called in the US. Never seen a hobber or shaper that had a correction mechanism for that, most places would just make a more accurate wormgear.

Maag grinders had mechanisms for altering the tooth shape, but that wasn't for correcting spacing errors.
 
I am curious about what you mean by pitch errors. Do you mean cyclic variations in the angular movement of the worm wheel for EACH turn of the worm?

Or what?
I think something has been lost in the translation. Perhaps asking about a hobber differential??????
 
Check out

Foundations of mechanical accuracy by Moore. Expensive book so best if you can borrow a copy.​

It's been a long time since I read it and I don't have a copy. But error correction on lead screwss were addressed.

Dave
 
Check out

Foundations of mechanical accuracy by Moore. Expensive book so best if you can borrow a copy.​

It's been a long time since I read it and I don't have a copy. But error correction on lead screws were addressed.
Lead screws on a hobber have nothing to do with pitch. The only time they could be involved in errors would be on the lead of a helical gear - and that's not cyclic, as his description would infer is the case he's talking about. So we can eliminate that.
 
Oh, I'm glad my question aroused interest!
Perhaps asking about a hobber differential??????
No, no, let's forget about the differential for now :)

All I can think is, he means tooth spacing errors.
To clarify what I mean, here's a small sketch:
Gear with error.JPG

For example, we want to machine a gear with Z=30. The angular pitch of the teeth is 360/30 = 12 degrees. Depending on the different accuracy classes of gears, two accuracy parameters related to the position of the teeth must be observed:
- maximum permissible angular pitch error between any two adjacent teeth
-maximum permissible total angular pitch error for any tooth

In the sketch above, I showed how the actual angular pitch between the teeth can change relative to the real one. Depending on the accuracy of the machine, the actual position of the teeth on workpiece may fluctuate + or - relative to the ideal one.
If we draw an analogy with a ball screw, then we have a maximum error within one turn of the screw and a maximum error at a certain length, usually 300 mm. For very precise screws, the maximum error along the entire length of the thread is standardized. Of course, in a situation with a worm wheel and a machine without a CNC, it is difficult to imagine the accumulated step error :)

If we return from this analogy to gears and machines for processing them, then in most non-CNC machines the main source of error in the angular position of the teeth is the worm gear that rotates the workpiece. The worm wheel has some clearance between the ideal tooth position and the actual tooth position. For example, in a wheel with Z=30, the 26th tooth should be located with an angular step relative to the first tooth (360/30)*26=312 degrees. But in fact, this tooth has a position, for example, 311.9972 degrees (minus 10 arc seconds). Of course, this error will be transmitted to the workpiece being processed. It is to compensate for errors in this part of the machine that the mechanisms I am talking about are designed.

most places would just make a more accurate wormgear.
Hehe, that's the problem - on which machine to make a more accurate worm wheel? The Soviet machines I found with a correction mechanism are designed specifically for finishing precision worm wheels. Here is its incomplete kinematic diagram:

spr_543_kin.jpg
The cams for correcting the error of the worm wheel (CAM1) and the worm (CAM2) are located on the right side of the image. The description says that the “ARM” lever rotates the planetary gear housing and additional movement is introduced into the kinematic connection. This movement will depend on the shape of CAM1 and CAM2.

Another analogy, only with other types of machines: pitch correction mechanisms on thread grinding machines or on machines for processing holes with precise coordinates.
On old thread grinding machines (I know for sure that this is not a Soviet feature :)) the nut from the ball screw, which moves the table with the workpiece, is fixed so that it can rotate. The nut has a radial pin that protrudes outward. The pin slides along a “guide” located nearby and installed +- parallel to the screw. The “guide” has the ability to tilt. Thus, if you change the inclination of this guide, then when the table moves, the nut will rotate slightly in + or - and correct the actual movement of the table. This is a simple circuit for correcting the accumulated pitch error, which allows you to compensate for the heating of the ball screw and similar errors. This mechanism looks very simplified like this:
Correction ball screw.JPG
Blue - ball screw; red - ball screw nut; green - nut pin; yellow - a spring between the machine table (which moves the nut) and the pin; gray - guide. On thread grinding machines I have only seen straight guides; on machines for processing holes with precise coordinates, these guides are slightly not straight to compensate for the error of the lead screw every inch, for example.
The “conversion coefficient” of this mechanism is such that, for example, to correct an error of 1 micron, the end of the pin needs to be lowered or raised by 0.1-0.2 mm - this can be achieved even with a file :)
On the gear grinding machine that I talked about in the initial post, the worm gear error correction system was more like a nut-turning circuit.
If I remember correctly, the correction guide was located around a worm wheel. A certain lever with a roller rode along this guide; the lever perceived different heights of the corrective guide, introduced additional movement into the kinematic diagram, and so on.

I'm sorry I had to write so many letters :rolleyes5:
 
Thanks for the explanation. I guess what threw me was it was a hob you were talking about. But I guess the gears and particularly the worm gear in a hobbing machine can have tooth errors just as a lead screw can errors from one turn to the next.

But now that begs the question, how do you measure those errors in order to know what correction is needed? Or better yet, how was that done 50 or 100 years ago?
 
But now that begs the question, how do you measure those errors in order to know what correction is needed? Or better yet, how was that done 50 or 100 years ago?
It's just tooth-to-tooth spacing, it's really easy. For power transmission cases it doesn't even matter that much, most of the accuracy is in the hob itself, you don't have to worry about the whole gear, just over any three teeth, and for extra-accurate stuff the best gear grinders did one tooth at a time then indexed; indexing is pretty well worked out.

The reason no one has seen this is because it's not very necessary or useful. Once in a while, for motion transmission like in a telescope or something maybe, but generally not for 99.837% of uses. Interesting but .... kinda like all those wacky engines people come up with.
 
Now you are confusing me again. Back in the original post, Machine Man said,

"Today I want to talk about the mechanisms for correcting angular pitch errors on machines for processing gears: gear hobbing machines or gear grinding machines with a grinding wheel in the form of a worm."

HOBBING or gear grinding with a HOB SHAPED GRINDING WHEEL is what we are discussing, or so I thought. A traditional hobbing machine uses a gear train to continuously rotate the gear being formed while the hob rotates to cut the teeth. And I can't but imagine that a gear grinding machine using a grinding wheel in the form of a worm (of a hob) would operate any different. So we are not indexing from tooth to tooth and able to apply a correction at each step. The gear blank is continuously rotating and the teeth in the gears of the gear train are continuously rotating. And each of those gears can have tooth-to-tooth errors. And the errors on one may, probably won't, have the same relationship to the errors on each of the others each time it rotates. So, you are going to have 2, 4, 6, 8, or more sets of errors, all OUT OF SYNC with each other and all contributing to the errors in the new gear being made.

Now, I know more than just a little bit about math. And to me, that sounds like a nightmare of a computational problem. And it had to be tackled BEFORE the age of digital computers. The very first thing I would do is try to find which gear had the most influence on the final product and start with that one. Then add in the others one at a time. But that would need to be done for each tooth count of a gear being cut. And if the gears in that gear train were disassembled and reassembled, even keeping the exact same gears in the exact same places in the gear train, then the process had to start over again due to synchronizing or the lack thereof. A mechanism was shown above that relied on the profile that was cut/hand filed into the edge of a linear cam. That could only compensate for one single state of the gear train. What about the next run to make another copy of the exact same gear? Did they back up the gear train to the original starting point so the errors repeated? Then they could measure the gear that was produced and make adjustments for it's errors. But backing up sounds very time consuming.

So I do ask, how they did it.

Oh, and I understand that the gearing in things like ordinary auto transmissions does need to be highly accurate in order to prolong their life. Was that "99.837%" number from some documented source or just off the top of your head?



It's just tooth-to-tooth spacing, it's really easy. For power transmission cases it doesn't even matter that much, most of the accuracy is in the hob itself, you don't have to worry about the whole gear, just over any three teeth, and for extra-accurate stuff the best gear grinders did one tooth at a time then indexed; indexing is pretty well worked out.

The reason no one has seen this is because it's not very necessary or useful. Once in a while, for motion transmission like in a telescope or something maybe, but generally not for 99.837% of uses. Interesting but .... kinda like all those wacky engines people come up with.
 
So I do ask, how they did it.

I was going to waste a whole bunch of both our time talking about this but let's cut to the chase -- because of the way hobs are made, and the way the tooth curve is generated, and the properties of an involute curve, this is not a problem. Which is why no one in the gear world has ever seen this thing. Think "research department at a university working on a problem that doesn't exist so they can write papers no one but other research twats read, in order to generate grants that keep themselves busy".

Was that "99.837%" number from some documented source or just off the top of your head?
Out of another part of the body :) But it's probably accurate these days. There's power transmission and there's motion transmission. Both are gears but the emphasis is on different aspects. Motion transmission would care about tooth-to-tooth spacing all around the gear, but look around you : do you see needles on dial faces anywhere these days ? People don't even like dial calipers, they all want digitals. You probably haven't seen a speedometer with a cable and gears in forty years. 99.837 may be optimistic :)

With power transmission, tooth-to-tooth spacing counts over a span of three teeth. If you're good over three, then over the entire part doesn't matter (for anything less than a turbo-jet, or nukular-powered naval steam turbine, that kind of thing). It doesn't matter because the load is carried over two to three teeth at any one time so if they are accurate enough that they go into and out of mesh smoothly, that'll work. In fact, there's a limit to how much accuracy counts there because the teeth bend as they get loaded then unloaded. So even if the spacing were absolutely perfect, under load it wouldn't be. Early in the 1900's peopel went to stub tooth teeth, they thought shorter was stronger but that was actually backwards. High strength teeth these days tend to be tall and skinny and they try for the max number of teeth in mesh so that when they do bend, there will be more teeth sharing the load and the in-and-out-of-mesh won't be so abrupt.

anyway, you can look at the finest tooth-cutting equipment ever made, stuff that will knock your socks off, Moore-quality and better, and it doesn't bother with this non-problem. So I'll leave now before you get even more bored :)
 
But now that begs the question, how do you measure those errors in order to know what correction is needed? Or better yet, how was that done 50 or 100 years ago?
The problems of measuring almost any precision that can be achieved on metal cutting machines were solved +- 100 years ago.
Specifically, in the case under consideration, the accuracy standards of metal-cutting machines contain 2 main checks regarding the accuracy of rotation of the table with the workpiece:
- table rotation accuracy
- accuracy of the processed part

First, a small digression - how much easier it has become to solve these problems today! The machine manufacturer can simply install an encoder with 12,000,000 pulses/rev and an error graph down to 0.1 arcseconds - and happily watch the result :) Then check the result with something like the Reni XR20 and continue to rejoice.

I'll try to describe a couple of "slightly more ancient" methods.
And so, I didn’t pretend to be a smart guy, and found an excellent book from 1952, which talks about the experience of one plant producing gear-processing machines in the field of increasing the kinematic accuracy of such machines. And of course about ways to measure kinematic accuracy.
It is worth saying that the USSR in 1952 is definitely not a place on the planet where there was a lot of advanced technology, so the methods described in this book most likely could have been implemented in Germany, Great Britain and the USA 100 years ago.

As for measuring a manufactured gear, this was definitely possible 100 years ago with an accuracy of about +-2 arcseconds.
Gear rotation is on a table with an aerostatic or hydrostatic bearing. Rotation angle measurement:
- theodolite and collimator
- collimator and multifaceted optical prism

With measurements while the machine is running, everything is, of course, much more complicated. This is what the communists proposed in 1952:
p0102.png
This is part of the measuring system that is installed near the machine table. f, d - precise rollers, evenly spaced on the circle and rotating with the machine table. They should be positioned with good accuracy, but a slight deviation in the position of each roller can be measured in advance (as I described above) and taken into account when measuring. a - a part with two contacts that are isolated from each other. This part can rotate and complete an electrical circuit through the rollers. To prevent contact wear due to electrical discharges, the current supplied to the line is small: about 0.25 mA and several volts.
p0103.png
And, this thing is an indicator :) 3 - a gas-discharge lamp with a round body; 1 - a cylinder made of sheet metal, a screw slot is made on the wall, this part rotates together with the machine spindle; 2 - a fixed cylinder with one straight slot along the axis; a scale is marked along the slot. Cylinder 1 is not directly connected to the rotation of the spindle, but through gears with the required gear ratio.
Both parts of the device are connected using a simple electronic unit based on vacuum tubes (yes, this all happened in 1952), which each time two rollers in the first part of the device are closed, sends a voltage pulse of short duration, about 1 ms, to the lamp.
These are, of course, simplified diagrams; the book contains more or less detailed drawings and a diagram of the electronic unit. And, what is most valuable - formulas and methods for working with the device and mathematical processing of the results. For example, several measurements, each time rotating the block with rollers by a small amount before starting the process - this allows you to calculate and eliminate the influence of instrument errors.
The final accuracy of measurements with this thing, based on the experience of measuring many instances of machines, different models, manufacturers, etc. - about 1-2-3 arc seconds.
And here are the results of introducing a correction device into various models of gear hobbing machines:
p0171.png

The photos are of course of terrible quality, after all, these are scans of a book from 1952. This is the correction device in the Pfauter RS2 division guitar:

p0133.png

In the designs of corrective devices proposed by the authors of the book, there are 4 corrective cams - 1 for correcting worm errors, one for correcting wheel errors. And two more - for a different direction of table rotation, because when reversed, the error map changes greatly.
Another interesting point. I looked more closely at the accuracy of the machine, whose kinematic diagram I gave above. And I'm a little shocked. The machine cuts worm wheels up to a diameter of 31 inches. The maximum kinematic error of table rotation is 2 seconds!!! The maximum accumulated error of the processed wheel metric module M=6 Z=102 D=24 inches is 8µm (6arcsec)!
 
The gear blank is continuously rotating and the teeth in the gears of the gear train are continuously rotating. And each of those gears can have tooth-to-tooth errors. And the errors on one may, probably won't, have the same relationship to the errors on each of the others each time it rotates. So, you are going to have 2, 4, 6, 8, or more sets of errors, all OUT OF SYNC with each other and all contributing to the errors in the new gear being made.

Now, I know more than just a little bit about math. And to me, that sounds like a nightmare of a computational problem. And it had to be tackled BEFORE the age of digital computers.
Actually, it's not all that scary :) Although about 1/4 of the book I'm currently studying is devoted to various mathematical calculations, the effect of idler gears on workpiece error is not that scary. The degree to which a gear will affect the rotation error of the table with the workpiece depends on the distance in the kinematic diagram of this gear from the main worm gear.
Look, for example, some terribly crooked gear in the division quadrant has an accumulated tooth pitch error of 1 degree. But this will lead to a rotation error of the machine table of 1/N, where N is Z of the main worm wheel. The situation is similar with the gears between the machine table and the correcting cams. Let’s say that due to errors in kinematics, “0” of the cam and “0” of the table are shifted relative to each other by +-1 degree. How much does the table rotation error change within +-1 degrees? Obviously, not by much. Here is an example of a table rotation error:
p0140.png
Which is why no one in the gear world has ever seen this thing.
I hope that maybe you can explain to me how in the USA (for example) they solved the chicken and egg problem? How to get an egg without a chicken?
I looked at the spare parts documentation for several gear hobbing machines and compared the claimed accuracy of these machines (based on accumulated tooth pitch error) with the accuracy of their main worm wheel. On average, the difference is about 2.5 times! To make a wheel with an error of 1 minute, we need a machine that will have a wheel inside with an error of 20 seconds! How to make this wheel?
In the case of lead screws, this problem was successfully solved by corrective devices. And I don't really understand how Pfauter, Reishauer or Gleason made worm wheels for their machines. Did they all modify their machines individually for similar purposes? But there are still a lot of consumers of super-precise gears, at least there were a lot of them 50 years ago.
 
I hope that maybe you can explain to me how in the USA (for example) they solved the chicken and egg problem? How to get an egg without a chicken?
It's not a problem, so they didn't have to solve it. This is the kind of thing people invent to keep themselves busy ... for extreme accuracy one coould use maag grinders, which don't use gears to space and develop the teeth. But even there, even if the teeth were perfectly spaced when coming off the grinder, in use they are not. Under load, teeth bend so they are never ever ever perfectly spaced. As they go into mesh they bend, as they leave mesh they unbend, the spacing is always affected.
 
I was told about it as it pertains to the pitch checking machine where the cut gear and a master were meshed and the graph shown was generated , rotation against displacement, I haven’t ever seen one of these calibration machines and only did the basic gear inspection , addendum dedendum, tooth width etc, and was introduced to the gear tooth vernier and setting tables, basics.
Taylor Hobson was mentioned and benson I think, old fashioned now I suppose.
Mark
 
I was told about it as it pertains to the pitch checking machine where the cut gear and a master were meshed and the graph shown was generated , rotation against displacement, I haven’t ever seen one of these calibration machines
We aim to please, you aim too, please :)

Photo is of a terrible example, looks like someone beat it with the ugly stick but easy to see how it works. Test piece goes between centers on the left, master gear is on an arbor on the right. Arbor is on a lightly-loaded pivot, which you crank into mesh with the gear under test. Rotate the workpiece one turn plus a tiny bit, the paper chart advances and a needle records deviation from perfect mesh. You can see runout, tooth spacing errors, and more with this type of functional test.

The other kind of testing is called "analytic" and charts deviation from a theoretically-perfect involute or deviation from the desired lead. They both have a place.

Obviously the weak point of the redliner is the need for a very accurate master gear, $$$. Conceivably, if your part is as accurate or more so than the master, then you ain't gonna get no info from the test ... but that's not usually a problem. Master gears are like jo blocks, accurate.

redliner.jpg
 








 
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